Introduction

This guide is the result of my experiences and will certainly be changed according to the needs.
As a new champion, I can't see Ahri's full potential but I believe we can do some complete and comprehensive guide with everybody's knowledges and comments.

Legend of the Nine Tails Fox

I will copy here some informations about the true Nine Tailed Fox legend because many of us are bored to see references to Naruto... I hope you'll enjoy it and you'll never compareAhri to Naruto again. =)

Introduction

The gumiho (literally "nine tailed fox") is a creature that appears in the oral tales and legends of Korea,[1] and are akin to European fairies. According to those tales, a fox that lives a thousand years turns into a gumiho, like its Japanese and Chinese counterparts (the kitsune and the huli jing).[2] It can freely transform, among other things, into a beautiful girl often set out to seduce men, and eat their liver. There are numerous tales in which the gumiho appears. Several of those can be found in the encyclopedic Compendium of Korean Oral Literature.

Transformation

A gumiho is a nine-tailed fox, a legendary creature with origins in ancient Chinese myths dating back centuries. There are versions of the figure in Chinese and Japanese folklore, although each differs slightly. The Chinese huli jing and the Japanese kitsune have more ambiguous moral compasses, in that they can be both good and bad, and are not necessarily out to get everyone. The Korean gumiho, on the other hand, is almost always a malignant figure, a carnivore who feasts on human flesh. Legends tell that while the gumiho is capable of changing its appearance, there is still something persistently fox-like about it; its countenance changes, but its nature does not. In Transformation of the gumiho, a gumiho transforms into an identical likeness of a bride at a wedding. Not even the bride's mother can tell the difference. The gumiho is only discovered when her clothes are removed. Bakh Mun-su and the gumiho records an encounter that Pak Munsu has with a girl, living alone in the woods, that has a fox-like appearance. In The Maiden who Discovered a gumiho through a Chinese Poem the gumiho was ultimately revealed when a hunting dog caught the scent of the fox and attacked. According to legend, a fox that lives a thousand years turns into a gumiho, a shape-shifter who can appear in the guise of a woman. A gumiho is evil by nature, and feeds on either human hearts or livers (different legends specify one or the other) in order to survive. The Chinese huli jing is said to be made up of feminine energy (yin) and needs to consume male energy (yang) to survive. The Japanese kitsune can be either male or female, and can choose to be quite benevolent.

The Korean gumiho is traditionally female. Some can hide their gumiho features, while other myths indicate that they can’t fully transform (ie. a fox-like face or set of ears, or the tell-tale nine tails). Either way there is usually at least one physical trait that will prove their true gumiho form, or a magical way to force them to reveal this form.

Much like werewolves or vampires in Western lore, there are always variations on the myth depending on the liberties that each story takes with the legend. Some tales say that if a gumiho abstains from killing and eating humans for a thousand days, it can become human. Others, like the drama Gumiho: Tale of the Fox’s Child, say that a gumiho can become human if the man who sees her true nature keeps it a secret for ten years. Regardless of each story’s own rules, a few things are always consistent: a gumiho is always a fox, a woman, a shape-shifter, and a carnivore. Now on to the cultural meanings. A fox is a common figure in many different cultures that represents a trickster or a smart but wicked creature that steals or outwits others into getting what it wants. Anyone who grew up on Aesop’s Fables knows the classic iteration of the fox figure in folklore. And it’s not hard to see how the fox got such a bad rap. The animal is a nocturnal hunter and a thief by nature, and is known the world over for its cunning mind. Although it is typically depicted as a woman when it transforms into a human being, the gumiho in the tale of The Maiden who Discovered a ***ino through a Chinese Poem turns into a young man that attempts to trick the maiden in marrying him. However, this is the only case in which it transforms into a man.

Although they are considered as having the ability to morph into other forms, the true identity of a gumiho was said to be zealously guarded by the gumihos themselves. There are also legends in which these transformations are said to be involuntary.

History

It is unclear at which point in time Koreans began viewing the gumiho as a purely evil creature, since many of the ancient texts mention benevolent Gumihos assisting humans. In fact, many older texts make more frequent mentions of wicked humans tricking kind but naïve Gumihos.

As the mythology of the Gumiho evolved, it was later believed that a Gumiho had to consume human hearts in order to survive. In later literature they are often depicted as a blood-thirsty half-fox, half-human creature that wandered cemeteries at night, digging human hearts out from graves.

Like all other monsters, the Gumiho was thought to grow wise with age and with enough training, eventually learn to morph itself into various forms, including humans. Thus, they are often depicted as beautiful young maidens that trick unsuspecting men and later consume their hearts.

Another version was that the Gumiho must eat livers. This was because the liver contained the energy of a human, meaning that it processes the food and gives energy, therefore making it the container of the life force of a human. The fairy tale The Fox Sister depicts a fox spirit preying on a family for livers.

Another version of the mythology, however, holds that with enough will a Gumiho could further ascend from its Yokwe state and become fully, permanently human and lose its evil character. Explanations of how this could be achieved vary, but they sometimes include aspects such as refraining from killing or tasting meat for a thousand days, or obtaining a cintamani and making sure that the Yeoiju saw the full moon at least every month during the ordeal. Unlike Yeoiju wielding dragons, Gumiho were not thought to be capable of omnipotence or creation at will since they were lesser creatures.

The idea of a beast becoming fully human is in fact quite heavily embedded in Korean mythology, such as the case in which a bear becomes a woman through a harsh ordeal in the Dangun mythology.

Runes

Why Greater Mark of Magic Penetration?
This is simple. More Magic Penetration means more damage.
According to the damage formula (math based on 5th rank of Orb of Deception), on a standard match up, i.e. a champion with 30 base MR, the efficiency of flat MPen will be visible starting from 182 AP if you stay at 7.83 Mpen (marks only). Admitting you buy Sorcerer's Shoes, you gain 15 flat MPen, meaning you have 22.83 flat MPen, in that case, your MPen will be effective starting at 76 AP.
If you have an MR tanky champions with 54.6 base MR like Mordekaiser, the efficiency of MPen vs AP will be visible with 7.83 Mpen (marks only) at 374 AP. If you have bought Sorcerer's Shoes, 254 AP.
Of course, flat MR reduction and % MR reduction or % Mpen reduce greatly the AP cap for the MPen efficiency. On champions with 54.6 MR, with 20 MR reduction (from Abyssal Mask), the efficiency of 22.83 flat MPen is visible starting from 108 AP.
And more you stack Magic Penetration and more you deal damage (Magic Resist and Armor are Logarithmics).

Cunning Mastery Tree:
I prefer Wanderer which can give you more mobility for ganks. Assassin is the only choice here. Especially because you will be alone most of the time until late game. Merciless is my preferred one because 5% more damage when enemy champion is below 40% may be more interesting than 1.5% mana regen as you shouldn't farm with abilities early to mid game. Bandit is useless for Ahri and Dangerous Game may be nice if you get a kill but got ignited.
Here the choice is hard. Precision gives 8.4 magic penetration at level 18. It is a nice bonus. Intelligence gives 5% CDR and increase the CDR cap by 5%. I selected Intelligence because the 5% bonus on CDR is great to reduce the cooldown on Spirit Rush and, so doing, be more versatile.
The main reason I decided to take Thunderlord's Decree is because the 2 other interesting choice for AP champions are Stormraider's Surge is not that useful as you have Spirit Rush and the effect of Deathfire Touch is halfed for AoE abilities and Orb of Deception is an AoE... Thunderlord's Decree also gives some decent damage bonus on enemy champion.

Items

Let's see in details how I stuffed Ahri.

First item to get is Doran's Ring.
15 AP, 100 HP and 5 mana per 5 seconds for less than 500 gold. More survivability, more mana regen for longer laning and some AP for decent damage. It is really one of the best item you can get early game.

Boots of Speed is an other possibility.
As Ahri needs mobility, boots allow to chase your opponent if you have any chance to gank (low HP or jungler's gank). Get some Health Potions for more survivability or you may take a Faerie Charm for more mana regen.

The last possibility, the one I don't recommend except if you're playing with a proactive jungler,is starting with The Dark Seal and a Health Potion. This is useful when you are certain to get early kills. Don't do this if you're not playing in duo queue or team.

The trinket you want will definitely be Warding Totem. Put a ward, save a (your) life.

When you first back to shop, buy Fiendish Codex. Why ? Simply because you'll get more AP, more CDR and you'll need it later. Then buy Sorcerer's Shoes which will allow you to chase or escape faster with some magic penetration bonus.

Mid game, I recommend to buy Morellonomicon first. This will help to have good mana regen and it will also offer you 20% CDR. The point with Ahri is to reach the CR cap at 40% CDR (or even 45% CDR with Intelligence ) as soon as possible. But in order to do a decent amount of damages, the second thing you will need is Rabadon's Deathcap obviously, more AP means more damages.

Summoner Spells

I recommand: Flash allows you to jump over walls either for gank or for escape. Ignite is a nice way to kill low health champions.

You can also use: Cleanse really effective against a team with lots of Crowd Control. Exhaust makes it easier to chase but you don't really need it. Ghost useful for both chasing or escaping. I recommand it if you don't choose Flash or Ignite. You may use it instead of Flash if you're an agressive player. Teleport Great spell for ganking, especially if your team use tons of wards. Barrier is nice if you feel focused often cause of an aggressive play but playing safe should be the best solution.

About Magic Resist Reduction & Magic Penetration

Once, somebody told me that Magic Penetration is not viable.
I gonna sum up here how important or not Magic Penetration is.

There are 3 ways to increase your magic damage:

Increase your base AP.

Increase your Magic Penetration.

Decrease enemy's Magic Resist.

First, let me explain how Magic Resist works.

Magic Resist

There is 2 formulas for Magic Damage calculation.
The first one is in case Magic Resist value greater than 0. This is most of the case.
The formula is: 100 / ( 100 + MR )
So, a champion with 50 MR should take only 100 / ( 100 + 50 ) = 66.6% of the damage.

The second one is in case Magic Resist value is less than 0. We will see later how it is possible.
The formula is: 2 - ( 100 / ( 100 - MR ) )
A champion with -20 MR should take 2 - ( 100 / ( 100 - ( -20 ) ) ) = 116.6% of damage.
This means, the magic damage should deal 16.6% more damage.

As Percentage MPen is applied last, it's effectiveness is reduced more you have Flat MPen and MR Reduction.

The base MR value for all champions at level 18 is between 30 and 54.6.
If they don't get MR stuff and assuming you don't have any MR Reduction nor Flat MPen, your Void Staff should reduce between 10 and 20 their MR efficiency.
But if any champion has, for exemple, 150 MR (Galio can have easily 200 MR), your Void Staff should reduce it's efficiency by 52.
My advice: Look at your enemies' stuff before going for Void Staff and in some case get an Abyssal Mask.

I've written a formula in order to simulate Ahri's skill damage at level 18 with different stats. All the stats I'm using is enemy's Magic Resist (MR), Ahri's Percentage and Flat Magic Resist Reduction (%MRR & FMRR) and Percentage and Flat Magic Penetration (%MPen & FMPen).

Late game you can farm quite fast and you will be able to push back minions assault but don't forget to be always able to use Flash or Spirit Rush in order to escape from ganks.

Tactical issue

How to escape ?
First commandment, try to survive! Don't die! When Ahri get Charm and as long as you are near tower, you can survive quite easily during early game.
That means when you are level 4, you can lead your opponont on your tower if they try to tower dive.
When level 6, you have both Flash and Spirit Rush for escaping or ganking. Try to keep at least one of these skills in order to escape ganks. Flash or Spirit Rush through wall or jungle if you see any danger.

Why going for more Movement Speed?
More mobility gives you more ease for chasing and can save your life especially against junglers or gankers like Udyr. If you want to see what I'm saying, look the video below.

How to get early kills and when?
In order to get some kills early game, you need to be patient. Harass your enemy and wait until level 6. When they're half life, you can try to rush him. When you're near enough use your Fox-Fire and then Spirit Rush, use Charm in order to pull him, then Orb of Deception to deal more damage and, at last Ignite if still not dead. Most of the time, it can kill anybody early game.
In some other case, you have greedy enemy. Thoses ones don't know how dangerous Ahri can be early game. (However be careful with jumpers like Le Blanc.) At level 3, you will be able to deal with Orb of Deception, Fox-Fire and Ignite around 300 damages.

How to gank top lane?
There is 2 possibilities. First one is if top pushed. go near their tower, Spirit Rush or Flash through the jungle and get the kill if low life. Escape again with Spirit Rush. Don't try your luck if he's not low HP.
If top is pushed, go through the brush and Charm him until you and top lane champ kill him. Chase with Spirit Rush if he tries to escape.

How to gank bottom lane?
Most of the time Supporter is bottom lane. There is always a ward here (except if they are really low elo...). In order to gank bottom lane, try to go when your team is pushed in order to help on your turret.
If your team push, try to go farther in order to last hit behind their turret. Escape with Spirit Rush if any enemy come. But be careful, don't be too greedy.

Why and where to ward?
"Put a ward, save a life", as we say. If you see where your opponents are going, you can move more efficiently. You can escape from ganks and their jungler won't be able to get a kill. Put at least a ward in both of the brush on middle lane's side.
If you have enough money, you can also put some wards in the jungle near you.

Team Work

Early jungler's gank
If you should have an active jungler who often gank mid, keep your Spirit Rush unless their ganker come (you should be able to rush to your turret if they try to gank you).
If their mid push and your jungler come, don't hesitate, as soon as the jungler engage, Spirit Rush or Flash to your target and Fox-Fire him. If not dead, he will be hardly injured and will go base.

Team gank
If you see any opportunity, you can gank bottom or top. Check your partners health, enemies' health and tower's health. If enemy isn't healthy, you can easily tower dive to help your team mate or to get the kill. Anyway, even if the enemy ran away, you can take down the tower faster and get more gold.Gank in jungle
Ahri is really great for ganks in jungle. With Charm you can CC any enemy champion for an almost free kill. But in order to do that, you need tons of wards. If your supporter do his job, it'll be pretty easy. If not, you need to buy few wards and to put them on tactical point: I mean brushes.

Summary

Ahri is a really good champion. Many way to escape ganks, great damage and a good CC.
If used properly, you can reverse any situation.

Even if my work is almost done, there is certainly much to write. Any comments are welcome so as any help or tips.